Prediction of Discretization of GMsFEM Using Deep Learning
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AbstractIn this paper, we propose a deep-learning-based approach to a class of multiscale problems. The generalized multiscale finite element method (GMsFEM) has been proven successful as a model reduction technique of flow problems in heterogeneous and high-contrast porous media. The key ingredients of GMsFEM include mutlsicale basis functions and coarse-scale parameters, which are obtained from solving local problems in each coarse neighborhood. Given a fixed medium, these quantities are precomputed by solving local problems in an offline stage, and result in a reduced-order model. However, these quantities have to be re-computed in case of varying media (various permeability fields). The objective of our work is to use deep learning techniques to mimic the nonlinear relation between the permeability field and the GMsFEM discretizations, and use neural networks to perform fast computation of GMsFEM ingredients repeatedly for a class of media. We provide numerical experiments to investigate the predictive power of neural networks and the usefulness of the resultant multiscale model in solving channelized porous media flow problems.
All Author(s) ListMin Wang, Siu Wun Cheung, Eric Chung, Yalchin Efendiev, Wing Tat Leung, Yating Wang
Journal nameMathematics
Year2019
Month5
Volume Number7
Issue Number5
PublisherMDPI
Article number412
ISSN2227-7390
eISSN2227-7390
LanguagesEnglish-United States

Last updated on 2020-08-08 at 01:20